Uniqueness of Kahler-Ricci solitons on compact Kahler manifolds

We introduce a new holomorphic invariant on any compact Kahler manifolds with positive first Chern class and nontrivial holomorphic vector fields, which contains the Futaki invariant as a special case. This invariant is shown to be an obstruction to the existence of Kahler-Ricci solitons. By solving a complex Monge-Ampere equation, we prove the uniqueness of Kahler-Ricci solitons. (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.